Shell models of energy cascade in turbulence

Annual Review of Fluid Mechanics

Volumn 35, Issue , 2003, Pages 441-468

  Biferale, Luca ^a  

^a INFM   (Italy)

Author keywords

Dynamical models; Multifractals

Indexed keywords

BOUNDARY CONDITIONS; CASCADES (FLUID MECHANICS); CORRELATION METHODS; FRACTALS; MATHEMATICAL MODELS; NUMERICAL ANALYSIS;

ENERGY HELICITY INTERACTIONS;

TURBULENCE;

CASCADE; FLUID DYNAMICS; FRACTAL ANALYSIS; MODEL; THREE-DIMENSIONAL FLOW; TURBULENCE;

EID: 0037861168     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fluid.35.101101.161122     Document Type: Article

References (88)

1. Andersen KH, Bohr T, Jensen MH, Nilsen JL, Olesen P. 2000. Pulses in the zero-spacing limit of the GOY model. Phys. D 138:44-62
2. Andersen KH, Muratore-Ginanneschi P. 1999. Shell model for time-correlated random advection of passive scalars. Phys. Rev. E 60:6663-81
3. Arad I, Biferale L, Celani A, Procaccia I, Vergassola M. 2001. Statistical conservation laws in turbulent transport. Phys. Rev. Lett. 87:164502-6
4. Aurell E, Boffetta G, Crisanti A, Frick P, Paladin G, Vulpiani A. 1994a. Statistical mechanics of shell models for 2-dimensional turbulence. Phys. Rev. E 50:4705-15
5. Aurell E, Boffetta G, Crisanti A, Paladin G, Vulpiani A. 1997. Predictability in the large: an extension of the concept of Lyapunov exponent. J. Phys. A 30:1-26
6. Aurell E, Frick P, Shaidurov V. 1994b. Hierarchical tree-model of 2-d turbulence. Phys. D 72:95-109
7. Belinicher VI, L'vov VS. 1987. J. Exp. Theor. Phys. 66:303-10
8. Belinicher VI, L'vov VS, Pomyalov A, Procaccia I. 1998. Computing the scaling exponents in fluid turbulence from first principles: demonstration of multiscaling. J. Stat. Phys. 93:797-832
9. Benzi R, Biferale L. 2002. Intermittency in turbulence. Proc. CISM School. Theory Turbul. In press
10. Benzi R, Biferale L, Parisi G. 1993. On intermittency in a cascade model for turbulence. Phys. D 65:163-71
11. Benzi R, Biferale L, Kerr R, Trovatore E. 1996a. Helical-shell models for three-dimensional turbulence. Phys. Rev. E 53:3541-50
12. Benzi R, Biferale L, Succi S, Toschi F. 1999. Intermittency and eddy-viscosities in dynamical models of turbulence. Phys. Fluids 11:1221-28
13. Benzi R, Biferale L, Toschi F. 1998. Multiscale correlation functions in turbulence. Phys. Rev. Lett. 80:3244-48
14. Benzi R, Biferale L, Tripiccione R, Trovatore E. 1996b. (1 + 1)-dimensional turbulence. Phys. Fluids 9:2335-63
15. Benzi R, Biferale L, Wirth A. 1997. Analytic calculation of anomalous scaling in random shell models for a passive scalar. Phys. Rev. Lett. 78:4926-29
16. Benzi R, Ciliberto S, Baudet C, Ruiz Chavarria G. 1995. On the scaling of three-dimensional homogeneous and isotropic turbulence. Phys. D 80:385-98
17. Benzi R, Paladin G, Parisi G, Vulpiani A. 1984. On the multifractal nature of fully developed turbulence and chaotic systems. J. Phys. A 17:3521-31
18. Biferale L, Blank M, Frisch U. 1994. Chaotic cascades with Kolmogorov 1941 scaling. J. Stat. Phys. 75:781-95
19. Biferale L, Boffetta G, Celani A, Lanotte A, Toschi F, Vergassola M. 2002. Isotropic and anisotropic decaying turbulence. Phys. Rev. Lett. Submitted
20. Biferale L, Boffetta G, Celani A, Toschi F. 1999. Multi-time multi-scale correlation function in turbulence and in turbulent models. Phys. D 127:187-97
21. Biferale L, Cencini M, Pierotti D, Vulpiani A. 1997. Intermittency in stochastically perturbed turbulent models. J. Stat. Phys. 88:1117-38
22. Biferale L, Daumont I, Dombre T, Lanotte A. 1999. Coherent structures in random shell models for passive scalar advection. Phys. Rev. E 60:R6299-302
23. Biferale L, Kerr R. 1995. Role of inviscid invariants in shell models of turbulence. Phys. Rev. E 52:6113-22
24. Biferale L, Lambert A, Lima R, Paladin G. 1995b. Transition to chaos in a shell model of turbulence. Phys. D 80:105-19
25. Biferale L, Pierotti D, Toschi F. 1998a. Helicity advection in turbulent models. J. Phys. 8:131-37
26. Biferale L, Pierotti D, Toschi F. 1998b. Helicity transfer in turbulent models. Phys. Rev. E 57:R2515-18
27. Biferale L, Pierotti D, Vulpiani A. 1998c. Time-reversible dynamical systems in turbulence. J. Phys. A 31:21-32
28. Boffetta G, Carbone V, Giuliani P, Veltri P, Vulpiani A. 1999. Power laws in solar flares: self-organized criticality or turbulence? Phys. Rev. Lett. 83:4662-65
29. Boffetta G, Giuliani P, Paladin G, Vulpiani A. 1998. An extension of the Lyapunov analysis for the predictability problem. J. Atmos. Sci. 55:3409-16
30. Bohr T, Jensen MH, Paladin G, Vulpiani A. 1998. Dynamical Systems Approach to Turbulence. Cambridge, UK: Cambridge Univ. Press
31. Borue V, Orszag SA. 1995. Force three-dimensional homogeneous turbulence with hyperviscosity. Europhys. Lett. 29:687-90
32. Borue V, Orszag SA. 1997. Spectra in helical three-dimensional homogeneous isotropic turbulence. Phys. Rev. E 55:7005-9
33. Brandemburg A. 1992. Energy spectra in a model for convective turbulence Phys. Rev. Lett. 69:605-8
34. Cao N, Chen S, She SZ. 1996. Scalings and the relative scalings in Navier-Stokes turbulence. Phys. Rev. Lett. 76:3711-14
35. Chkhetiani O. 1996. On the triple correlations in helical turbulence JETP Lett. 63:808-12
36. Daumont I, Dombre T, Gilson JL. 2000. Instanton calculus in shell models of turbulence. Phys. Rev. E 62:3592-610
37. Desnyansky VN, Novikov EA. 1974. The evolution of turbulence spectra to the similarity regime. Izv. Akad. Nauk. SSSR Fiz. Atmos. Okeana 10:127-36
38. Ditlevsen PD. 1997. Cascades of energy and helicity in the GOY shell model of turbulence. Phys. Fluids 9:1482-84
39. Ditlevsen PD, Mogensen IA. 1996. Cascades and statistical equilibrium in shell models of turbulence. Phys. Rev. E 53:4785-93
40. Eggers J, Grossman S. 1991. Anomalous turbulent velocity scaling from the Navier-Stokes equation. Phys. Lett. A 156:444-49
41. Eyink G. 1993a. Lagrangian field-theory, multifractals and universal scaling in turbulence. Phys. Lett. A 172:355-60
42. Eyink G. 1993b. Renormalization group and operator product expansion in turbulence-shell models. Phys. Rev. E 48:1823-38
43. Eyink G. 1994. Large-N limit of the spherical model of turbulence. Phys. Rev. E 49:3990-4002
44. Fairhall AL, L'vov VS, Procaccia I. 1998. Dissipative scaling functions in Navier-Stokes turbulence: experimental tests. Europhys. Lett. 43:277-83
45. Falkovich G, Gawedzki K, Vergassola M. 2001. Particles and fields in fluid turbulence. Rev. Mod. Phys. 73:913-75
46. Frick P, Dubrulle B, Babiano A. 1995. Scaling properties of a class of shell models. Phys. Rev. E 51:5582-93
47. Frisch U. 1995. Turbulence: The Legacy of A.N. Kolmogoro. Cambridge, UK: Cambridge Univ. Press
48. Gawedzki K, Kupiainen A. 1995. Anomalous scaling of the passive scalar. Phys. Rev. Lett 75:3834-37
49. Giuliani P, Carbone V. 1998. A note on shell models for MHD turbulence. Europhys. Lett. 43:527-32
50. Gledzer EB. 1973. System of hydrodynamic type admitting two quadratic integrals of motion. Sov. Phys. Dokl. 18:216-17
51. Grossmann S, Lohse D. 1994. Scale resolved untermittency in turbulence. Phys. Fluids A 6:611-17
52. Jensen MH, Paladin G, Vulpiani A. 1991. Intermittency in a cascade model for 3-dimensional turbulence. Phys. Rev. A 43:798-805
53. Jensen MH, Paladin G, Vulpiani A. 1992. Shell model for turbulent advection of passive-scalar fields. Phys. Rev. A 45:7214-21
54. Kadanoff L, Lohse D, Schorghofer N. 1997. Scaling and linear response in the GOY turbulence model. Phys. D 100:165-86
55. Kadanoff L, Lohse D, Wang J, Benzi R. 1995. Scaling and dissipation in the GOY shell model. Phys. Fluids 7:617-29
56. Kolmogorov AN. 1962. A refinement of previous hypothesis concerning the local structyure of turbulence in a viscous incompressible fluid at high Reynolds number. J. Fluid Mech. 13:82-85
57. Kraichnan RH. 1994. Anomalous scaling of a randomly advected passive scalar. Phys. Rev. Lett. 72:1016-19
58. Landau LD, Lifshitz EM. 1987. Fluid Mechanics. Oxford: Pergamon. 2nd ed.
59. Lorenz EN. 1972. Deterministic nonperiodic flow. J. Atmos. Sci. 20:130-41
60. L'vov V, Podivilov E, Pomyalov A, Procaccia I, Vandembroucq D. 1998a. Improved shell model of turbulence. Phys. Rev. E 58:1811-22
61. L'vov VS, Podivilov E, Procaccia I. 1997. Temporal multiscaling in hydrodynamic turbulence. Phys. Rev. E 55:7030-35
62. L'vov VS, Procaccia I. 1996a. Fusion rules in turbulent systems with flux equilibrium. Phys. Rev. Lett. 76:2898-901
63. L'vov VS, Procaccia I. 1996b. Towards a non-perturbative theory of hydrodynamic turbulence: Fusion rules, exact bridge relations, and anomalous viscous scaling functions. Phys. Rev. E 54:6268-84
64. L'vov SV, Procaccia I. 2000. Analytic calculation of the anomalous exponents in turbulence: using the fusion rules to flush out a small parameter. Phys. Rev. E 62:8037-57
65. L'vov VS, Procaccia I, Vandembroucq D. 1998b. Universal scaling exponents in shell models of turbulence: viscous effects are finite-sized corrections to scaling. Phys. Rev. Lett. 81:802-5
66. Mandelbrot B. 1977. Intermittent turbulence in self-similar cascades: divergence of high moments and dimension of the carrier. J. Fluid Mech. 62:331-58
67. Meneveau C, Sreenivasan KR. 1987. The multifractal spectrum of the dissipation field in turbulent flows. Nucl. Phys. B Proc. Suppl. 2:49-76
68. Moffat HK. 1969. The degree of knotedness of tangled vortex lines. J. Fluid Mech. 35:117-29
69. Moffat HK, Tsinober A. 1992. Helicity in laminar and turbulent flows. Annu. Rev. Fluid Mech. 24:281-312
70. Mordant N, Metz P, Michel O, Pinton JF. 2001. Measurement of Lagrangian velocity in fully developed turbulence. Phys. Rev. Lett. 87:214501-4
71. Muzy JF, Bacry E, Arneoodo A. 1993. Multifractal formalism for fractal signals: the structure functions approach versus the waelet-transform modulus-maximum method. Phys. Rev. E 47:875-84
72. Nakano T. 1988. Direct interaction approximation of turbulence in the wave packet representation. Phys. Fluids 31:1420-28
73. Noullez A, Wallace G, Lempert W, Miles RB, Frisch U. 1997. Transverse velocity increments in turbulent flow using the RELIEF technique. J. Fluid Mech. 339:287-307
74. Ohkitani K, Yamada M. 1989. Temporal intermittency in the energy cascade process and local Lyapunov analysis in fully developed model of turbulence. Prog. Theor. Phys. 89:329-41
75. O'Neil J, Meneveau C. 1993. Spatial correlations in turbulence: predictions from the multifractal formalism and comparison with experiments. Phys. Fluids A 5:158-72
76. Parisi G, Frisch U. 1985. On the singularity structure of fully deeloped turbulence. In Turbulence and Predictability in Geophysical Fluid Dynamics, ed. M Ghil, R Benzi, G Parisi, pp. 84-87. Varenna: Int. School Phys.
77. Pierotti D. 1997. Intermittency in the large N - limit of a spherical shell model for turbulence. Europhys. Lett. 37:323-28
78. Pierotti D, L'vov VS, Pomyalov A, Procaccia I. 2000. Anomalous scaling in a model of hydrodynamic turbulence with a small parameter. Europhys. Lett. 50:473-79
79. Pisarenko D, Biferale L, Courvoisier D, Frisch U, Vergassola M. 1993. Further results on multifractality in shell models. Phys. Fluids A 5:2533-38
80. Pope SB. 2000. Turbulent Flows. Cambridge, UK: Cambridge Univ. Press
81. Renner C, Peinke J, Friedrich R. 2001. Experimental indications for Markov properties of small-scale turbulence. J. Fluid Mech. 433:383-409
82. Siggia ED. 1978. Model of intermittency in three-dimensional turbulence. Phys. Rev. A 17:1166-76
83. Stolovitzky G, Sreenivasan KR. 1994. Kolmogorov's refined similarity hypothesis for turbulence and general stochastic processes. Rev. Mod. Phys. 66:229-40
84. van de Water W, Herweijer J. 1996. Anomalous scaling and anisotropy in turbulence Phys. Scr. T 67: 136-40
85. Vergassola M. 1996. Anomalous scaling for passively advected magnetic fields. Phys. Rev. E 53:R3021-24
86. Waleffe F. 1992. The nature of triad interactions in homogeneous turbulence. Phys. Fluids 4:350-63
87. Waleffe F. 1993. Inertial transfers in the helical decomposition Phys. Fluids 5:677-85
88. Wirth A, Biferale L. 1996. Anomalous scaling in random shell models for passive scalars. Phys. Rev. E 54:4982-89